# Thread: help with integrating factor equation

1. ## help with integrating factor equation

hi

i have been given the attached question to work through and i just cant get my head around it (sorry its an attachment, i can not work out how to display it within this message).

any help/pointers you could give would be great

thanks

2. Originally Posted by wallsst
hi

i have been given the attached question to work through and i just cant get my head around it (sorry its an attachment, i can not work out how to display it within this message).

any help/pointers you could give would be great

thanks
i think, there was a mistake.. Q is not 2.5t but (5-2.5t)

anyways, i'll put a solution here..

i have to find the temp at time $\displaystyle T$ if $\displaystyle T=60^o$ when t=0 using $\displaystyle \frac{dT}{dt} + 0.1T = e^{0.1t}$
and the integrating factor is given by $\displaystyle = \exp \left[ {\int_0^t {0.1 \, d\tau}} \right] = \exp (0.1t) = e^{0.1t}$

so, $\displaystyle T= \dfrac{1}{e^{0.1t}} \left( {60^o + \int_0^t e^{0.1\tau }\left( {5-2.5\tau } \right)} \, d\tau \right)$

the integral part can be solved using integration by parts once..

3. thanks, after a few hours of looking at it, it did finally click and, as you said, Q is (5-2.5t)

cheers for the help